One of the major problems in quantum physics has been to generalize classical root-mean-square error measurements obtain an measure satisfying both soundness (to vanish for any accurate measurements) and completeness only measurements). A noise-operator based commonly used this purpose, but it turned out incomplete. Recently, Ozawa proposed a new definition be sound complete. Here, we present n...

Recent years have witnessed a controversy over Heisenberg’s famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. We discuss two approaches to adapting the classic notion of root-mean-square error to quantum measurements. One is based on the concept of noise operator; it...

In this paper we compute the root-mean-square (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant γ provides an upper bound on the RMS gain whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of γ-dependent algebraic Riccati equations. The...

Bures distance holds a special place among various measures due to its several distinguished features and finds applications in diverse problems quantum information theory. It is related fidelity and, other things, it serves as bona fide measure for quantifying the separability of states. In this work, we calculate exact analytical results mean root square between fixed density matrix random ma...